微扰代数量子场论与重整化群
Perturbative Algebraic Quantum Field Theory and the Renormalization Groups
摘要：
本文发展了一种新的代数量子场论微扰构造形式。形式主义允许治疗的低维理论和非多项式的相互作用。讨论了描述微扰结构中自由度的Stueckelberg-Petermann重整化群与不同尺度理论的Wilson思想之间的联系。特别是，我们涉及的方法重整化的Polchinski的流量方程的爱泼斯坦-格拉泽方法。我们还表明，重整化群的意义上的盖尔曼-低（它的特点下的所有尺度的变化的行为的理论）是一个1-参数子群的Stueckelberg-Petermann群，这个子群一般只是一个cocycle。由于Stueckelberg-Petermann群的代数结构不依赖于全局量，因此这个群可以在绝热极限下被公式化，而不需要满足任何红外发散。特别是，我们推导出一个代数版本的Callan-Symanzik方程，并定义在一个状态独立的方式的β函数。
英文摘要：
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the Stueckelberg-Petermann renormalization group which describes the freedom in the perturbative construction with the Wilsonian idea of theories at different scales . In particular we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method. We also show that the renormalization group in the sense of Gell-Mann-Low (which characterizes the behaviour of the theory under the change of all scales) is a 1-parametric subfamily of the Stueckelberg-Petermann group and that this subfamily is in general only a cocycle. Since the algebraic structure of the Stueckelberg-Petermann group does not depend on global quantities, this group can be formulated in the (algebraic) adiabatic limit without meeting any infrared divergencies. In particular we derive an algebraic version of the Callan-Symanzik equation and define the beta-function in a state independent way.
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